Solution of Correlated Multi-Response Optimization Problem

2010 ◽  
Vol 1 (4) ◽  
pp. 22-46 ◽  
Author(s):  
Saurav Datta ◽  
Goutam Nandi ◽  
Asish Bandyopadhyay ◽  
Pradip Kumar Pal
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Desirability Function ◽  
Optimization Technique ◽  
Principal Component ◽  
Optimization Techniques ◽  
Individual Response ◽  
Bead Geometry ◽  
Taguchi Optimization ◽  
Response Optimization

This paper highlights an integrated approach to solve the correlated multi-response optimization problem through a case study in submerged arc welding (SAW). The proposed approach has been presented to overcome different limitations and drawbacks of existing optimization techniques available in literature. Traditional Taguchi optimization technique is based under the assumption that quality responses are independent to each other; however, this assumption may not always be valid. A common trend in the solution of a multi-objective optimization problem is to convert these multi-objectives into an equivalent single objective function. While deriving this equivalent objective function, different weightage are assigned to different responses according to their relative priority. In this regard, it seems that no specific guideline is available for assigning individual response weighs. To avoid this, Principal Component Analysis (PCA) has been adopted to eliminate correlation among individual desirability values and to calculate uncorrelated quality indices that have been aggregated to calculate overall grey relational grade. This study combines PCA, Desirability Function (DF) approach, and grey relation theory to the entropy measurement technique. Finally, the Taguchi method has been used to derive optimal process environment capable of producing desired weld quality related to bead geometry.

Solution of Correlated Multi-Response Optimization Problem

2012 ◽  
pp. 61-79
Author(s):  
Saurav Datta ◽  
Goutam Nandi ◽  
Asish Bandyopadhyay ◽  
Pradip Kumar Pal
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Desirability Function ◽  
Optimization Technique ◽  
Principal Component ◽  
Integrated Approach ◽  
Bead Geometry ◽  
Taguchi Optimization ◽  
Entropy Measurement ◽  
Response Optimization

This paper highlights an integrated approach to solve the correlated multi-response optimization problem through a case study in submerged arc welding (SAW). The proposed approach has been presented to overcome different limitations and drawbacks of existing optimization techniques available in literature. Traditional Taguchi optimization technique is based under the assumption that quality responses are independent to each other; however, this assumption may not always be valid. A common trend in the solution of a multi-objective optimization problem is to convert these multi-objectives into an equivalent single objective function. While deriving this equivalent objective function, different weightage are assigned to different responses according to their relative priority. In this regard, it seems that no specific guideline is available for assigning individual response weighs. To avoid this, Principal Component Analysis (PCA) has been adopted to eliminate correlation among individual desirability values and to calculate uncorrelated quality indices that have been aggregated to calculate overall grey relational grade. This study combines PCA, Desirability Function (DF) approach, and grey relation theory to the entropy measurement technique. Finally, the Taguchi method has been used to derive optimal process environment capable of producing desired weld quality related to bead geometry.

scholarly journals A novel desirability function for multi-response optimization and its application in chemical engineering

2020 ◽  
Vol 26 (3) ◽  
pp. 309-319
Author(s):  
Velibor Marinkovic
Keyword(s):  
Chemical Engineering ◽  
Desirability Function ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
The Other ◽  
Individual Response ◽  
Differentiable Functions ◽  
Modern Engineering ◽  
Gradient Based ◽  
Response Optimization

In many aspects of modern engineering (processes, products, and systems)InIn many aspects of modern engineering (processes, products, and systems) there is a need to optimize multiple responses simultaneously, rather than optimizing one response at a time. The optimization of each individual response may generate as many different results as the responses, which is considered in the study. Then, it may be impossible to decide whether one solution is better than the other. On the other hand, some improvement in one response can significantly degrade at least one or more responses. There are a number of multi-response optimization techniques available. Among these multi-response optimization techniques, the desirability-based approaches take a prominent place because they are less sophisticated, easy to understand and implement, and more flexible with respect to other existing approaches, due to which they are very popular among researchers and practitioners. There are many different formulations of the desirability function. Unfortunately, most desirability functions known in the literature are piecewise, non-differentiable functions. In this paper, a novel desirability function is proposed, which is continuous and differentiable in its domain. This function is more suitable for applying some of the efficient gradient-based optimization methods. The efficiency and accuracy of the proposed method were analyzed on two chemical processes that were studied extensively in the literature.

scholarly journals An Optimized Protection Coordination Scheme for the Optimal Coordination of Overcurrent Relays Using a Nature-Inspired Root Tree Algorithm

2018 ◽  
Vol 8 (9) ◽  
pp. 1664 ◽  
Author(s):  
Abdul Wadood ◽  
Saeid Gholami Farkoush ◽  
Tahir Khurshaid ◽  
Chang-Hwan Kim ◽  
Jiangtao Yu ◽  
...  
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Operating Time ◽  
Global Optimum ◽  
Optimization Techniques ◽  
Tree Algorithm ◽  
Engineering Problems ◽  
Overcurrent Relays ◽  
Optimal Coordination ◽  
Root Tree

In electrical engineering problems, bio- and nature-inspired optimization techniques are valuable ways to minimize or maximize an objective function. We use the root tree algorithm (RTO), inspired by the random movement of roots, to search for the global optimum, in order to best solve the problem of overcurrent relays (OCRs). It is a complex and highly linear constrained optimization problem. In this problem, we have one type of design variable, time multiplier settings (TMSs), for each relay in the circuit. The objective function is to minimize the total operating time of all the primary relays to avoid excessive interruptions. In this paper, three case studies have been considered. From the simulation results, it has been observed that the RTO with certain parameter settings operates better compared to the other up-to-date algorithms.

scholarly journals Expensive multi-objective optimization of electromagnetic mixing in a liquid metal

2020 ◽  
Author(s):  
Sebastian Prinz ◽  
Jana Thomann ◽  
Gabriele Eichfelder ◽  
Thomas Boeck ◽  
Jörg Schumacher
Keyword(s):  
Objective Function ◽  
Permanent Magnet ◽  
Optimization Problem ◽  
Trust Region Method ◽  
Rigid Bodies ◽  
Optimization Techniques ◽  
Computational Time ◽  
Homogeneous Distribution ◽  
Mean Flow ◽  
Steady Streaming

Abstract This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet located underneath the rectangular vessel. The rectangular magnet provides a spatially non-uniform magnetic field that is known analytically. The magnet oscillation creates a steady mean flow (steady streaming) similar to those observed from oscillating rigid bodies. In the optimization problem, randomly distributed mass-less particles are advected by the flow to achieve a homogeneous distribution (objective function 1) while keeping the work done to move the permanent magnet minimal (objective function 2). A single evaluation of these two objective functions may take more than two hours. For that reason, to save computational time, the proposed method uses interpolation models on trust-regions for finding descent directions. We show that, even for our significantly simplified model problem, the mixing patterns vary significantly with the control parameters, which justifies the use of improved optimization techniques and their further development.

Bead Geometry Optimization of Submerged Arc Weld: Exploration of Weighted Principal Component Analysis (WPCA)

2011 ◽  
Vol 110-116 ◽  
pp. 790-798 ◽  
Author(s):  
A. Biswas ◽  
S. Bhaumik ◽  
Gautam Majumdar ◽  
Saurav Datta ◽  
S.S. Mahapatra
Keyword(s):  
Principal Component Analysis ◽  
Taguchi Method ◽  
Principal Components ◽  
Principal Component ◽  
Component Analysis ◽  
Optimization Techniques ◽  
Confirmatory Test ◽  
Bead Geometry ◽  
Weighted Principal Component ◽  
Submerged Arc

The present work attempts to overcome underlying assumptions in traditional Taguchi based optimization techniques highlighted in literature. Taguchi method alone fails to solve multi-response optimization problems. In order to overcome this limitation, exploration of grey relation theory, desirability function approach, utility theory etc. have been found amply applied in literature in combination with Taguchi method. But aforesaid approaches relies on the assumption that individual response features are uncorrelated i.e. independent of each other which are really impossible to happen in practice. The study takes into account this response correlation and proposes an integrated methodology in a case study on optimization of multiple bead geometry parameters of submerged arc weldment. Weighted Principal Component Analysis (WPCA) has been applied to eliminate response correlation and to convert correlated responses into equal or less number of uncorrelated quality indices called principal components. Based on individual principal components a Multi-response Performance Index (MPI) has been introduced to derive an equivalent single objective function which has been optimized (maximized) using Taguchi method. Experiments have been conducted based on Taguchi’s L25 Orthogonal Array design with combinations of process control parameters: voltage, wire feed, welding speed and electrode stick-out. Different bead geometry parameters: bead width, bead height, penetration depth and HAZ dimensions have been optimized. Optimal result has been verified by confirmatory test. The study highlights effectiveness of the proposed method for solving multi-objective optimization of submerged arc weld.

scholarly journals Some applications of a novel desirability function in simultaneous optimization of multiple responses

2021 ◽  
Vol 49 (3) ◽  
pp. 534-548
Author(s):  
Velibor Marinković
Keyword(s):  
Comparative Analysis ◽  
Desirability Function ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
The Other ◽  
Simultaneous Optimization ◽  
Desirability Functions ◽  
Gradient Based ◽  
Response Optimization ◽  
Optimization Methodology

In the framework of multi-response optimization techniques, the optimization methodology based on the desirability function is one of the most popular and most frequently used methodologies by researchers and practitioners in engineering, chemistry, technology and many other fields of science and technique. Numerous desirability functions have been introduced to improve the performance of this optimization methodology. Recently, a novel desirability function for multi-response optimization is proposed, which is smooth, nonlinear, and differentiable, and thus more suitable for applying some of the more efficient gradient-based optimization methods. This paper evaluates the performance of the proposed method through six real examples. After a comparative analysis of the results, it is shown that the proposed method in a certain measure outperforms the other competitive optimization methods.

Multi-objective performance investigation of orthopaedic bone drilling using Taguchi membership function

2017 ◽  
Vol 231 (12) ◽  
pp. 1133-1139 ◽  
Author(s):  
Gurmeet Singh ◽  
Vivek Jain ◽  
Dheeraj Gupta
Keyword(s):  
Membership Function ◽  
Bone Cells ◽  
Optimization Technique ◽  
Real Life ◽  
Multiple Response ◽  
Bone Drilling ◽  
Taguchi Optimization ◽  
Response Characteristics ◽  
Response Optimization ◽  
Single Response

Orthopaedic bone drilling attacks the surrounded bone cells and tissues in terms of thermal and mechanical in such a way that these cells can get damaged permanently. This damage to the surrounding of drill point upsurges the rehabilitation time of injury and in some cases leads to the failure of the bone screw joint. This study is based on the optimization of multiple response characteristics to minimize the damage during the bone drilling. All real-life problems, including bone drilling, require the multiple response optimization for getting a combined optimization result for all countable response characteristics. The Taguchi optimization technique is observed as a highly recommended tool for single response optimization. This article uses the Taguchi technique with little modification of membership function that will help to convert the multiple response characteristics into single response and further optimize it as a single function of performance. Rotational speed, feed rate of tool at three different levels with three different kinds of drilling tools are the drilling parameters selected for the study. The objective of this study is to minimize the surface roughness and thrust force simultaneously. Analysis of variance helps to find the percentage contribution and significance of each parameter on the performance.

Simultaneous optimization of output parameters in HPC drilling using multi response optimization technique with desirability function approach

2020 ◽  
Vol 17 (3) ◽  
pp. 437-444
Author(s):  
Hanmant Virbhadra Shete ◽  
Madhav S. Sohani
Keyword(s):  
Mathematical Models ◽  
Response Surface ◽  
Desirability Function ◽  
Optimization Technique ◽  
Simultaneous Optimization ◽  
Drilling Process ◽  
Content Type ◽  
Input Parameters ◽  
Response Optimization ◽  
Desirability Function Approach

Purpose This paper aims to examine an investigation of high-pressure coolant (HPC) drilling process with regard to experimental models of output parameters, effect of input parameters on output parameters and simultaneous optimization of the output parameters. Design/methodology/approach Experimental plan was designed using response surface method and experiments were conducted on HPC drilling set up. Measurements for output parameters were carried out and mathematical models were obtained. Multi response optimization using a composite desirability function approach was used to obtain optimum values of input parameters for simultaneous optimization of output parameters. Findings Optimal value of input parameters for optimization of HPC drilling process were obtained as; coolant pressure: 21 bar, spindle speed: 3,970 rpm, feed rate: 0.084 mm/rev and peck depth: 5.50 mm. The composite desirability obtained is 0.9412, which indicates that the performance of HPC drilling process was significantly optimized. Developed mathematical models of the output parameters accurately represent the entire design space under investigation. Originality/value This is the first study that involves variation of higher coolant pressure and investigation of HPC drilling process using response surface methodology and multi response optimization technique with desirability function.

An Objective Function for Optimization Techniques in Simultaneous Multiple-Element Analysis by Inductively Coupled Plasma Spectrometry

1982 ◽  
Vol 36 (1) ◽  
pp. 37-40 ◽  
Author(s):  
J. J. Leary ◽  
A. E. Brookes ◽  
A. F. Dorrzapf ◽  
D. W. Golightly
Keyword(s):  
Objective Function ◽  
Inductively Coupled Plasma ◽  
Optimization Technique ◽  
Optimization Techniques ◽  
Operating Conditions ◽  
Objective Functions ◽  
Element Analysis ◽  
Plasma Spectrometry ◽  
Inductively Coupled ◽  
Inductively Coupled Plasma Spectrometry

This work considers several composite objective functions and uses the sequential simplex optimization technique to evaluate the performance of a proposed objective function in locating optimal instrumental operating conditions for simultaneous multiple-element determinations by inductively coupled plasma spectrometry. The proposed objective function, combined with a generalized approach to optimization, can be applied to any group of analysis elements and is of value in routine optimization procedures for simultaneous multiple-element methods of analysis.

scholarly journals A Novel Hybrid Sine Cosine Algorithm and Pattern Search for Optimal Coordination of Power System Damping Controllers

2022 ◽  
Vol 14 (1) ◽  
pp. 541
Author(s):  
Mahdiyeh Eslami ◽  
Mehdi Neshat ◽  
Saifulnizam Abd. Khalid
Keyword(s):  
Power Systems ◽  
Power System ◽  
Objective Function ◽  
Time Domain ◽  
Optimization Problem ◽  
Optimization Technique ◽  
Pattern Search ◽  
Optimal Coordination ◽  
Sine Cosine Algorithm ◽  
Nonlinear Time Domain

This paper presents an effective hybrid optimization technique based on a chaotic sine cosine algorithm (CSCA) and pattern search (PS) for the coordinated design of power system stabilizers (PSSs) and static VAR compensator (SVC)-based controllers. For this purpose, the design problem is considered as an optimization problem whose decision variables are the controllers’ parameters. Due to the nonlinearities of large, interconnected power systems, methods capable of handling any nonlinearity of power networks are preferable. In this regard, a nonlinear time domain-based objective function was used. Then, the proposed hybrid chaotic sine cosine pattern search (hCSC-PS) algorithm was employed for solving this optimization problem. The proposed method employed the global search ability of SCA and the local search ability of PS. The performance of the new hCSC-PS was investigated using a set of benchmark functions, and then the results were compared with those of the standard SCA and some other methods from the literature. In addition, a case study from the literature is considered to evaluate the efficiency of the proposed hCSC-PS for the coordinated design of controllers in the power system. PSSs and additional SVC controllers are being considered to demonstrate the feasibility of the new technique. In order to ensure the robustness and performance of the proposed controller, the objective function is evaluated for various extreme loading conditions and system configurations. The numerical investigations show that the new approach may provide better optimal damping and outperforms previous methods. Nonlinear time-domain simulation shows the superiority of the proposed controller and its ability in providing efficient damping of electromechanical oscillations.

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